Here is an attempt with FullGraphics, a very old function:
FullGraphics
fg = FullGraphics[Plot[x, {x, -1, 1}, GridLines -> Automatic]] Graphics[GeometricTransformation[fg[[1]], ShearingTransform[Pi/4, {1, 0}, {0, 1}]]]
Try this:
p = Plot[x, {x, -1, 1}, GridLines -> Automatic]; ImageForwardTransformation[p,ShearingTransform[Pi/4,{1,0},{0,1}],PlotRange->All]
Thanks to both. Never heard of either of those functions.